This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A064337 #22 Apr 10 2024 14:33:48
%S A064337 2,5,11,17,29,41,59,79,101,127,157,191,229,271,317,367,421,487,557,
%T A064337 631,709,787,877,967,1061,1163,1277,1381,1489,1601,1721,1861,1993,
%U A064337 2131,2273,2423,2579,2741,2909,3079,3253,3433,3617,3821,4019,4217,4421,4637
%N A064337 Minimal prime numbers with increasing prime differences.
%H A064337 Harry J. Smith, <a href="/A064337/b064337.txt">Table of n, a(n) for n = 1..1000</a>
%F A064337 a(1) = 2, a(n+1) = MIN {prime p | p >= a(n) + prime(n)} (where prime(n) is the n-th prime number).
%F A064337 Conjecture: a(n) ~ K*n^2*log(n). - _Bill McEachen_, Apr 04 2024
%F A064337 a(n) >= A007504(n) >> n^2 log n. On Cramér's conjecture, a(n) << n^2 log^2 n. - _Charles R Greathouse IV_, Apr 10 2024
%e A064337 a(5) = 29, since a(4) = 17, p(4) = 7 and 29 is the smallest prime which is not smaller than 17 + 7.
%t A064337 NextPrime[n_] := (k = n; While[ ! PrimeQ[k], k++ ]; k); f[1] = 2; f[n_] := NextPrime[ f[n - 1] + Prime[n-1] ]; Table[ f[n], {n, 1, 50} ]
%t A064337 Transpose[NestList[{First[#]+1,NextPrime[Last[#]+Prime[First[#]]]}&, {1,2}, 50]][[2]] (* _Harvey P. Dale_, Oct 23 2011 *)
%o A064337 (PARI) for (n=1, 1000, if (n>1, a=nextprime(a + prime(n - 1)), a=2); write("b064337.txt", n, " ", a) ) \\ _Harry J. Smith_, Sep 12 2009
%Y A064337 Cf. A064336.
%K A064337 easy,nonn
%O A064337 1,1
%A A064337 _Lior Manor_, Sep 13 2001